Comparison between the MHFEM formulation and a 2 nd spatial order FV formulation of the linear groundwater flow problem

Mixed and Mixed Hybrid Finite Elements (MHFE) methods have been widely used in the last decade for simulation of groundwater flow problem, petroleum reservoir problems, potential flow problems, etc. The main advantage of these methods is that, unlike the classical Galerkin approach, they guarantee local and global mass balance, as well the flux continuity between inter-element sides. The simple shape of the control volume, where the mass conservation is satisfied, makes also easier to couple this technique with a Finite Volume technique in the time splitting approach for the solution of advection-dispersion problems. In the present paper a new second spatial approximation order Finite Volume formulation (FV2) for triangular irregular meshes, is proposed for the solution of the linear groundwater flow problem and the numerical results are compared with the corresponding one given by a MHFE method. It can be shown that the FV2 approach is equivalent to the MHFE approach in the case of isotropic medium and regular or mildly irregular mesh, but has a smaller number of unknowns and better matrix properties. In the case of irregular mesh, an approximation is proposed to maintain the superior matrix properties of the FV2 approach, with the consequent introduction of a small error in the computed solution. Key-Words: groundwater, finite elements method, mixed hybrid finite elements method, finite volumes method, positivedefinite matrix, M-property, Raviart-Thomas basis function